On a certain sum, C.I. is Rs 41 and SI is Rs 40. for 2 years. What is the rate p.a

Supposing that Rs is rupees, CI is compound interest over two years, SI is simple interest in two years, and p.a. means per annum,

1 rupee interest was earned on the first year's interest, during the second year.

Let S be the original invested sum and r be the annual rate.

S*r = 20
S*r^2 = 1
r = 1/20 = 5%
S = 20 Rs

How 20 came

You are right.I made a mistake in the last step

S*r = S*0.05 = 20
S = 400 Rs

Plse do it again,

u have really confuse me

I would do it the same up to and including

r = 1/20 = 5%
After that, I made a mistake which you pointed out. The derivation should finish with
S*r = S*0.05 = 20
S = 400 Rs

The first year's interest earned is $20. If that is compounded in the second year, the interest earned in the second year is 0.05*(420) = 21, for a two-year total of 41, as required.

In the simple interest (SI) case, you just earn $20 a year in interest, indefinitely. Unless the interest is withdrawn annually, and reinvested or put to good use, this is not a good way to save money.

if r is to be calculated , then how u can directly say r = .05%

To find the rate per annum (p.a.), we can use the formula for calculating interest:

Simple Interest (SI) = (Principal) x (Rate) x (Time)

In this case, we are given that the Simple Interest (SI) is Rs 40 and for a period of 2 years. However, the question also mentions that the Compound Interest (C.I.) for the same period and principal amount is Rs 41. This suggests that the interest is compounded annually.

Now, we can set up the equation using the given information:

SI = C.I. = Rs 40
Rate = ?
Time = 2 years

As we have the compound interest (C.I.), we can use the formula to calculate it:

C.I. = Principal x [(1 + Rate/100)^Time - 1]

Substituting the given values:

41 = Principal x [(1 + Rate/100)^2 - 1]

Next, we can simplify the equation by dividing both sides by the Principal:

(1 + Rate/100)^2 - 1 = 41/Principal

Since the Principal is not provided in the question, we need additional information to solve for the rate. If you have the principal amount or any other relevant information, please provide it to proceed with the calculation.